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Searching for Diophantine quintuples

Volume 173 / 2016

Mihai Cipu, Tim Trudgian Acta Arithmetica 173 (2016), 365-382 MSC: Primary 11D09; Secondary 11B37, 11J86, 11D45. DOI: 10.4064/aa8254-2-2016 Published online: 18 May 2016

Abstract

We consider Diophantine quintuples $\{a, b, c, d, e\}$. These are sets of positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured that there are no Diophantine quintuples; we improve on current estimates to show that there are at most $5.441\cdot 10^{26}$ Diophantine quintuples.

Authors

  • Mihai CipuSimion Stoilow Institute of Mathematics
    of the Romanian Academy
    Research unit no. 5, P.O. Box 1-764
    RO-014700 Bucureşti, Romania
    e-mail
  • Tim TrudgianMathematical Sciences Institute
    The Australian National University
    Canberra, Australia
    e-mail

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